Discontinuous Groups in the Plane
The chapter starts with a discussion of abstract discontinuous groups, but is primarily concerned with discontinuous groups of fractional linear transformations acting on the extended complex plane. We discuss some inequalities, including Jørgensen’s inequality, the limit set, and fundamental domains, in particular, the Ford region. The point of view here is primarily one complex dimensional; real higher dimensional discontinuous groups will be discussed in Chapter IV.
KeywordsRiemann Surface Limit Point Distinct Element Fundamental Domain Kleinian Group
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